In algebra, the method of substitution is used to simplify problems by reducing the number of variables or quantities. The specific details of the solution depend on the original problem.
A classic case of algebraic substitution is an expression and the value of a variable, for example, x + 5 with x = 10. To evaluate the first expression, substitute the given value of x to find (10) + 5 = 15. Because x and 10 are the same value, the x in the initial expression can be replaced with 10 and a value can be found.
Another example in which substitution can be used to solve an algebraic expression is in the case of a system of linear equations. Consider the following; x + y = 10 and x - y = 6. Substitution can be used to solve the system by first solving the second equation for x as follows, x = 6 + y, and then substituting this expression for x into the first equation as follows, (6 + y) + y = 10, so 2y = 4, and y = 2. Use substitution once more to replace either equation's y variable with the value 2 to find x + (2) = 10, so x = 8.